Hydrodynamics of Superfluid Bose Gases in an Optical Lattice at Finite Temperatures

Starting from an effective action for the order parameter field, we derive a coupled set of generalized hydrodynamic equations for a Bose condensate in an optical lattice at finite temperatures. Using the linearized hydrodynamic equations, we study the microscopic mechanism of the Landau instability due to the collisional damping process between the condensate and noncondensate atoms. It is shown that the Landau criterion for the stability of a superfluid in a uniform system is modified due to the presence of the periodic optical lattice potential.